Good quality icons from low quality images

I'm trying to make icons out of this image. I've tried to improve the quality of it but sharpening/blur/changing the colour balance etc, but I'm not happy with the end product. I used to use Photoshop Elements 2 but recently I got Photoshop 7 and I'm still getting used to it. Are there any functions in Photoshop that I can use to improve the quality of that picture? Or are there any other ways I can improve the quality?

These are the icons I have made (but I'm not happy with them)


Also, I've noticed that some graphics I have made look good in photoshop, but once I have saved them/uploaded them, the quality decreases. Can anyone tell me why that happens?

Thank you.